A234787 Cubes (with at least two digits) that become squares when their rightmost digit is removed.

1000, 64000, 729000, 4096000, 15625000, 46656000, 117649000, 262144000, 531441000, 1000000000, 1771561000, 2985984000, 4826809000, 7529536000, 11390625000, 16777216000, 24137569000, 34012224000, 47045881000, 64000000000

Offset

1,1

Comments

With the help of the Nagell-Lutz theorem it is easy to prove that there are no other solutions than those of the form 1000*n^6.

Links

Georg Fischer, Table of n, a(n) for n = 1..300 [a(1..204) from Reiner Moewald]

Wikipedia, Nagell-Lutz theorem.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

a(n) = 1000*n^6.

From Colin Barker, Dec 15 2019: (Start)

G.f.: 1000*x*(1 + x)*(1 + 56*x + 246*x^2 + 56*x^3 + x^4) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Prog

(PARI) lista(nn) = {for (n=1, nn, if (((cb = n^3) > 10) && issquare(cb\10), print1(cb, ", ")); ); } \\ Michel Marcus, Jan 10 2014
(PARI) Vec(1000*x*(1 + x)*(1 + 56*x + 246*x^2 + 56*x^3 + x^4) / (1 - x)^7 + O(x^40)) \\ Colin Barker, Dec 15 2019

Crossrefs

Cf. A226354.

Subsequence of A000578.

Sequence in context: A117690 A186936 A185747 * A379591 A029799 A029779

Adjacent sequences: A234784 A234785 A234786 * A234788 A234789 A234790

Keyword

nonn,base,easy

Author

Reiner Moewald, Dec 30 2013

Status

approved